Analysis of mean-square error and transient speed of the LMS adaptive algorithm

For the least mean square (LMS) algorithm, we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state. We establish the convergence of the second-order statistics as the number of iterations increases...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 48; no. 7; pp. 1873 - 1894
Main Authors: Dabeer, O., Masry, E.
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2002
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive filters
Adaptive signal processing
Algorithms
Asymptotic properties
Convergence of numerical methods
Correlation
Ergodic processes
Error analysis
Errors
Filtering
Information theory
Least mean square methods
Least mean squares algorithm
Markov processes
Matrices
Regression
Statistics
Transient analysis
Wiener filtering
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:For the least mean square (LMS) algorithm, we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state. We establish the convergence of the second-order statistics as the number of iterations increases, and we derive the exact asymptotic expressions for the mean square errors. In particular, the result for the excess signal estimation error gives conditions under which the LMS algorithm outperforms the Wiener filter with the same number of taps. We also analyze a new measure of transient speed. We do not assume a linear regression model: the desired signal and the data process are allowed to be nonlinearly related. The data is assumed to be an instantaneous transformation of a stationary Markov process satisfying certain ergodic conditions.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2002.1013131